Yes, they definitely can. The best way is if the economics and math behind the token is designed in a way that it stimulates natural growth with time. Provided that adoption and demand of the token increase.

The team can also manipulate the price by bying or selling its own tokens on exchanges. For example, Canya recently announced they will buyback a portion of their tokens.

Legit projects should care about price movement and early investors and guarantee a min low of the price on the exchanges.